/usr/include/rheolef/field_vf_expr_dg.h is in librheolef-dev 6.6-1build2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 | #ifndef _RHEOLEF_FIELD_VF_EXPR_DG_H
#define _RHEOLEF_FIELD_VF_EXPR_DG_H
///
/// This file is part of Rheolef.
///
/// Copyright (C) 2000-2009 Pierre Saramito <Pierre.Saramito@imag.fr>
///
/// Rheolef is free software; you can redistribute it and/or modify
/// it under the terms of the GNU General Public License as published by
/// the Free Software Foundation; either version 2 of the License, or
/// (at your option) any later version.
///
/// Rheolef is distributed in the hope that it will be useful,
/// but WITHOUT ANY WARRANTY; without even the implied warranty of
/// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
/// GNU General Public License for more details.
///
/// You should have received a copy of the GNU General Public License
/// along with Rheolef; if not, write to the Free Software
/// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
///
/// =========================================================================
//
// field_vf_expr_dg: discontinuous Galerkin operators
// in expressions templates for variationnal formulations
//
/*
SPECIFICATION: a first example
Let v be a function defined over Omega
and discontinuous accross internal sides (e.g. Pkd).
Let f be a function defined on Oemga.
We want to assembly
l(v) = int_{internal sides} f(x) [v](x) ds
where [v] is the jump of v accross internal sides.
=> l(v) = sum_{K is internal sides} int_K f(x) [v](x) ds
Let K be an internal side of the mesh of Omega.
int_K f(x) [v](x) ds
= int_{hat_K} f(F(hat_x))
[v](F(hat_x))
det(DF(hat_x)) d hat_s
where F is the piola transformation from the reference element hat_K to K:
F : hat_K ---> K
hat_x |--> x = F(hat_x)
The fonction v is not defined on a basis over internal sides K but over
elements L of the mesh of Omega.
Let L0 and L1 the two elements such that K is the common side of L0 and L1
and K is oriented from L0 to L1:
[v] = v0 - v1 on K, where v0=v/L0 and v1=v/L1.
Let G0 the piola transformation from the reference element tilde_L to L0:
G0 : tilde_L ---> L0
tilde_x |--> x = G0(tilde_x)
Conversely, let G1 the piola transformation from the reference element tilde_L to L1.
int_K f(x) [v](x) ds
= int_{hat_K} f(F(hat_x))
(v0-v1)(F(hat_x))
det(DF(hat_x)) d hat_s
The the basis fonction v0 and v1 are defined by using tilde_v, on the reference element tilde_L:
v0(x) = tilde_v (G0^{-1}(x))
v1(x) = tilde_v (G1^{-1}(x))
and with x=F(hat_x):
v0(F(hat_x)) = tilde_v (G0^{-1}(F(hat_x)))
v1(F(hat_x)) = tilde_v (G1^{-1}(F(hat_x)))
Thus:
int_K f(x) [v](x) ds
= int_{hat_K} f(F(hat_x))
( tilde_v (G0^{-1}(F(hat_x)))
- tilde_v (G1^{-1}(F(hat_x))) )
det(DF(hat_x)) ds
Observe that H0=G0^{-1}oF is linear:
H0 : hat_K ---> tilde0_K subset tilde_L
hat_x ---> tilde0_x = H0(hat_x)
Conversely:
H1 : hat_K ---> tilde1_K subset tilde_L
hat_x ---> tilde1_x = H1(hat_x)
Thus, K linearly transforms by H0 into a side tilde0_K of the reference element tilde_L
and, by H1, into another side tilde1_K of tilde_L.
int_K f(x) [v](x) ds
= int_{hat_K} f(F(hat_x))
( tilde_v (H0(hat_x))
- tilde_v (H1(hat_x)) )
det(DF(hat_x)) ds
Let (hat_xq, hat_wq)_{q=0...} a quadrature formulae over hat_K.
The integral becomes:
int_K f(x) [v](x) ds
= sum_q f(F(hat_xq))
( tilde_v (H0(hat_xq))
- tilde_v (H1(hat_xq)) )
det(DF(hat_xq)) hat_wq
Then, the basis functions tilde_v can be computed one time for all
over all the sides tilde(i)_K of the reference element tilde_L, i=0..nsides(tilde_L)
at the quadratures nodes tilde(i)_xq = Hi(hat_xq):
tilde_v (Hi(hat_xq)), i=0..nsides(tilde_L), q=0..nq(hat_K)
SPECIFICATION: a second example
We want to assembly
l(v) = int_{internal sides} f(x) [grad(v).n](x) ds
where [grad(v).n] is the jump of the normal derivative of v accross internal sides.
Let K be an internal side of the mesh of Omega.
int_K f(x) [grad(v).n](x) ds
= int_{hat_K} f(F(hat_x))
[grad(v).n](F(hat_x))
det(DF(hat_x)) d hat_s
= int_{hat_K} f(F(hat_x))
(grad(v0).n)(F(hat_x))
det(DF(hat_x)) d hat_s
- int_{hat_K} f(F(hat_x))
(grad(v1).n)(F(hat_x))
det(DF(hat_x)) d hat_s
where v0=v/L0 and v1=v/L1 and Li are the two elements containing the side K.
Let us fix one of the Li and omits the i subscript.
The computation reduces to evaluate:
int_K f(x) grad(v).n(x) ds
= sum_q f(F(hat_xq))
(grad(v).n)(F(hat_xq))
det(DF(hat_xq)) hat_wq
From the gradient transformation:
grad(v)(F(hat_xq)) = DG^{-T}(H(hat_xq)) * tilde_grad(tilde_v)(H(hat_xq))
where H = G^{-1}oF is linear from hat_K to tilde_K subset tilde_L.
int_K f(x) grad(v).n(x) ds
= sum_q f(F(hat_xq))
DG^{-T}(H(hat_xq))*tilde_grad(tilde_v)(H(hat_xq))
.n(F(hat_xq))
det(DF(hat_xq)) hat_wq
We can evaluate one time for all the gradients of basis functions tilde_v
on the quadrature nodes of each sides tilde_K of tilde_L :
tilde_grad(tilde_v)(H(hat_xq))
The piola basis functions and their derivatives are also evaluated one time for all on these nodes :
DG^{-T}(H(hat_xq))
The normal vector
n(xq), xq=F(hat_xq), q=...
should be evaluated on K, not on L that has no normal vector.
IMPLEMENTATION: bassis evaluation => test.cc
The basis_on_pointset class extends to the case of an integration over a side of
test_rep<T,M>::initialize (const geo_basic<float_type,M>& dom, const quadrature<T>& quad, bool ignore_sys_coord) const {
_basis_on_quad.set (quad, get_vf_space().get_numbering().get_basis());
_piola_on_quad.set (quad, get_vf_space().get_geo().get_piola_basis());
=> inchange'
}
test_rep<T,M>::element_initialize (const geo_element& L, size_type loc_isid=-1) const {
if (loc_isid != -1) {
basis_on_quad.restrict_on_side (tilde_L, loc_isid);
piola_on_quad.restrict_on_side (tilde_L, loc_isid);
}
}
test_rep<T,M>::basis_evaluate (...) {
// Then, a subsequent call to
basis_on_quad.evaluate (tilde_L, q);
// will restrict to the loc_isid part.
}
IMPLEMENTATION: normal vector => field_vf_expr.h & field_nl_expr_terminal.h
on propage des vf_expr aux nl_expr le fait qu'on travaille sur une face :
class nl_helper {
void element_initialize (const This& obj, const geo_element& L, size_type loc_isid=-1) const {
obj._nl_expr.evaluate (L, isid, obj._vector_nl_value_quad);
}
};
pour la classe normal :
field_expr_terminal_normal::evaluate (L, loc_isid, value) {
if (loc_isid != -1) K=side(L,loc_isid); else K=L;
puis inchange.
}
pour la classe terminal_field: si on evalue un field uh qui est discontinu :
on sait sur quelle face il se restreint :
field_expr_terminal_field::evaluate (L, loc_isid, value) {
if (loc_isid != -1) {
_basis_on_quad.restrict_on_side (tilde_L, loc_isid);
}
for (q..) {
general_field_evaluate (_uh, _basis_on_quad, tilde_L, _dis_idof, q, value[q]);
}
}
IMPLEMENTATION: bassis evaluation => basis_on_pointset.cc
c'est la que se fait le coeur du travail :
basis_on_pointset::restrict_on_side (tilde_L, loc_isid)
=> initialise
a l'initialisation, on evalue une fois pour tte
sur toutes les faces en transformant la quadrature via
tilde(i)_xq = Hi(hat_xq)
tilde(i)_wq = ci*hat_wq
avec
ci = meas(tilde(i)_K)/meas(hat_K)
puis :
basis_on_pointset::evaluate (tilde_L, q)
on se baladera dans la tranche [loc_isid*nq, (loc_isid+1)*nq[
du coup, on positionne un pointeur de debut q_start = loc_isid*nq
et une taille q_size = nq
si les faces sont differentes (tri,qua) dans un prisme, il faudra
un tableau de pointeurs pour gerer cela :
q_start [loc_nsid+1]
q_size [loc_isid] = q_start[loc_isid+1] - q_start[loc_isid]
basis_on_pointset::begin() { return _val[_curr_K_variant][_curr_q].begin() + q_start[_curr_K_variant][loc_isid]; }
basis_on_pointset::begin() { return _val[_curr_K_variant][_curr_q].begin() + q_start[_curr_K_variant][loc_isid+1]; }
et le tour est joue' !
PLAN DE DEVELOPPEMENT:
1) DG transport
basis_on_pointset.cc
test.cc
essais :
lh = integrate(jump(v)*f);
convect_dg2.cc
2) DG diffusion : avec normale et gradient
field_vf_expr.h
class nl_helper
field_nl_expr_terminal.h
field_expr_terminal_normal::evaluate (L, loc_isid, value)
field_expr_terminal_field ::evaluate (L, loc_isid, value)
*/
#include "rheolef/field_vf_expr.h"
namespace rheolef {
// ---------------------------------------------------------------------------
// class dg
// ---------------------------------------------------------------------------
template<class Expr, class VfTag = typename Expr::vf_tag_type>
class field_vf_expr_dg {
public:
// typedefs:
typedef typename Expr::size_type size_type;
typedef typename Expr::memory_type memory_type;
typedef typename Expr::value_type value_type;
typedef typename Expr::scalar_type scalar_type;
typedef typename Expr::float_type float_type;
typedef typename Expr::space_type space_type;
typedef VfTag vf_tag_type;
typedef typename details::dual_vf_tag<vf_tag_type>::type
vf_dual_tag_type;
typedef field_vf_expr<Expr,VfTag> self_type;
typedef field_vf_expr<typename Expr::dual_self_type,vf_dual_tag_type>
dual_self_type;
// alocators:
field_vf_expr_dg (const Expr& expr, const float_type& c0, const float_type& c1)
: _expr0(expr),
_expr1(expr),
_c0(c0),
_c1(c1),
_tilde0_L0(),
_tilde1_L1(),
_bgd_omega()
{
}
// accessors:
const space_type& get_vf_space() const { return _expr0.get_vf_space(); }
static const space_constant::valued_type valued_hint = Expr::valued_hint;
space_constant::valued_type valued_tag() const { return _expr0.valued_tag(); }
size_type n_derivative() const { return _expr0.n_derivative(); }
// mutable modifiers:
void initialize (const geo_basic<float_type,memory_type>& dom, const quadrature<float_type>& quad, bool ignore_sys_coord) const {
_expr0.initialize (dom, quad, ignore_sys_coord);
_expr1.initialize (dom, quad, ignore_sys_coord);
_bgd_omega = get_vf_space().get_geo().get_background_geo();
check_macro (_bgd_omega == dom.get_background_geo(),
"discontinuous Galerkin: incompatible integration domain "<<dom.name() << " and test function based domain "
<< get_vf_space().get_geo().name());
}
void initialize (const band_basic<float_type,memory_type>& gh, const quadrature<float_type>& quad, bool ignore_sys_coord) const {
_expr0.initialize (gh, quad, ignore_sys_coord);
_expr1.initialize (gh, quad, ignore_sys_coord);
fatal_macro ("unsupported discontinuous Galerkin on a band"); // how to define background mesh _bgd_omega ?
}
void element_initialize (const geo_element& K) const;
template<class ValueType>
void basis_evaluate (const reference_element& hat_K, size_type q, std::vector<ValueType>& value) const;
template<class ValueType>
void valued_check() const {
check_macro (get_vf_space().get_numbering().is_discontinuous(),
"unexpected continuous test-function in space " << get_vf_space().stamp()
<< " for jump or average operator (HINT: omit jump or average)");
_expr0.valued_check<ValueType>();
}
protected:
// data:
mutable Expr _expr0;
mutable Expr _expr1;
scalar_type _c0;
scalar_type _c1;
mutable reference_element _tilde0_L0;
mutable reference_element _tilde1_L1;
mutable geo_basic<float_type,memory_type> _bgd_omega;
};
// ---------------------------------------------------------------------------
// basis_evaluate
// ---------------------------------------------------------------------------
template<class Expr, class VfTag>
template<class ValueType>
void
field_vf_expr_dg<Expr,VfTag>::basis_evaluate (
const reference_element& hat_K,
size_type q,
std::vector<ValueType>& value) const
{
size_type loc_ndof0 = _expr0.get_vf_space().get_constitution().loc_ndof (_tilde0_L0),
loc_ndof1 = 0;
if (_tilde1_L1.variant() != reference_element::max_variant) {
loc_ndof1 = _expr1.get_vf_space().get_constitution().loc_ndof (_tilde1_L1);
}
check_macro (loc_ndof0+loc_ndof1 == value.size(),
"unexpected value.size="<<value.size()<<": expect size="<<loc_ndof0+loc_ndof1
<< " for ValueType="<<typename_macro(ValueType)<<" and valued=" << _expr1.get_vf_space().valued());
std::vector<ValueType> value0 (loc_ndof0),
value1 (loc_ndof1);
_expr0.basis_evaluate (_tilde0_L0, q, value0);
// average (i.e. _c0==0.5): fix it on the boundary where c0=1 : average(v)=v on the boundary
Float c0 = (_tilde1_L1.variant() != reference_element::max_variant || _c0 != 0.5) ? _c0 : 1;
for (size_type loc_idof = 0; loc_idof < loc_ndof0; ++loc_idof) {
value[loc_idof] = c0*value0 [loc_idof];
}
if (_tilde1_L1.variant() != reference_element::max_variant) {
_expr1.basis_evaluate (_tilde1_L1, q, value1);
for (size_type loc_idof = 0; loc_idof < loc_ndof1; ++loc_idof) {
value[loc_idof+loc_ndof0] = _c1*value1 [loc_idof];
}
}
}
// ---------------------------------------------------------------------------
// element_initialize
// ---------------------------------------------------------------------------
template<class Expr, class VfTag>
void
field_vf_expr_dg<Expr,VfTag>::element_initialize (const geo_element& K) const
{
size_type L_map_d = K.dimension() + 1;
size_type L_dis_ie0, L_dis_ie1;
side_information_type sid0, sid1;
L_dis_ie0 = K.master(0);
L_dis_ie1 = K.master(1);
check_macro (L_dis_ie0 != std::numeric_limits<size_type>::max(),
"unexpected isolated mesh side K="<<K);
if (L_dis_ie1 != std::numeric_limits<size_type>::max()) {
// K is an internal side
const geo_element& L0 = _bgd_omega.dis_get_geo_element (L_map_d, L_dis_ie0);
const geo_element& L1 = _bgd_omega.dis_get_geo_element (L_map_d, L_dis_ie1);
L0.get_side_informations (K, sid0);
L1.get_side_informations (K, sid1);
_tilde0_L0 = L0;
_tilde1_L1 = L1;
// methode "non-const": provoque une copie physique au 1er appel (c'est ce qu'il faut)
_expr0.element_initialize_on_side (L0, sid0);
_expr1.element_initialize_on_side (L1, sid1);
} else {
// K is a boundary side
const geo_element& L0 = _bgd_omega.dis_get_geo_element (L_map_d, L_dis_ie0);
L0.get_side_informations (K, sid0);
_tilde0_L0 = L0;
_tilde1_L1 = reference_element::max_variant;
_expr0.element_initialize_on_side (L0, sid0);
}
}
} // namespace rheolef
#endif // _RHEOLEF_FIELD_VF_EXPR_DG_H
|